#include"mrrr.h"
/* Subroutine */int pdlarrb(int *n, double *d__, double *lld, int *ifirst,
		int *ilast, double *rtol1, double *rtol2, int *offset, double *w,
		double *wgap, double *werr, double *work, int *iwork, double *pivmin,
		double * spdiam, int *twist, int *info) {
	/* System generated locals */
	int i__1;
	double d__1, d__2;


	/* Local variables */
	int i__, k, r__, i1, ii, ip;
	double gap, mid, tmp, back, lgap, rgap, left;
	int iter, nint, prev, next;
	double cvrgd, right, width;
	int negcnt;
	double mnwdth;
	int olnint, maxitr;

	/*  -- LAPACK auxiliary routine (version 3.2) -- */
	/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
	/*     November 2006 */

	/*     .. Scalar Arguments .. */
	/*     .. */
	/*     .. Array Arguments .. */
	/*     .. */

	/*  Purpose */
	/*  ======= */

	/*  Given the relatively robust representation(RRR) L D L^T, DLARRB */
	/*  does "limited" bisection to refine the eigenvalues of L D L^T, */
	/*  W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial */
	/*  guesses for these eigenvalues are input in W, the corresponding estimate */
	/*  of the error in these guesses and their gaps are input in WERR */
	/*  and WGAP, respectively. During bisection, intervals */
	/*  [left, right] are maintained by storing their mid-points and */
	/*  semi-widths in the arrays W and WERR respectively. */

	/*  Arguments */
	/*  ========= */

	/*  N       (input) int */
	/*          The order of the matrix. */

	/*  D       (input) DOUBLE PRECISION array, dimension (N) */
	/*          The N diagonal elements of the diagonal matrix D. */

	/*  LLD     (input) DOUBLE PRECISION array, dimension (N-1) */
	/*          The (N-1) elements L(i)*L(i)*D(i). */

	/*  IFIRST  (input) int */
	/*          The index of the first eigenvalue to be computed. */

	/*  ILAST   (input) int */
	/*          The index of the last eigenvalue to be computed. */

	/*  RTOL1   (input) DOUBLE PRECISION */
	/*  RTOL2   (input) DOUBLE PRECISION */
	/*          Tolerance for the convergence of the bisection intervals. */
	/*          An interval [LEFT,RIGHT] has converged if */
	/*          RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) */
	/*          where GAP is the (estimated) distance to the nearest */
	/*          eigenvalue. */

	/*  OFFSET  (input) int */
	/*          Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET */
	/*          through ILAST-OFFSET elements of these arrays are to be used. */

	/*  W       (input/output) DOUBLE PRECISION array, dimension (N) */
	/*          On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are */
	/*          estimates of the eigenvalues of L D L^T indexed IFIRST throug */
	/*          ILAST. */
	/*          On output, these estimates are refined. */

	/*  WGAP    (input/output) DOUBLE PRECISION array, dimension (N-1) */
	/*          On input, the (estimated) gaps between consecutive */
	/*          eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between */
	/*          eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST */
	/*          then WGAP(IFIRST-OFFSET) must be set to ZERO. */
	/*          On output, these gaps are refined. */

	/*  WERR    (input/output) DOUBLE PRECISION array, dimension (N) */
	/*          On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are */
	/*          the errors in the estimates of the corresponding elements in W. */
	/*          On output, these errors are refined. */

	/*  WORK    (workspace) DOUBLE PRECISION array, dimension (2*N) */
	/*          Workspace. */

	/*  IWORK   (workspace) int array, dimension (2*N) */
	/*          Workspace. */

	/*  PIVMIN  (input) DOUBLE PRECISION */
	/*          The minimum pivot in the Sturm sequence. */

	/*  SPDIAM  (input) DOUBLE PRECISION */
	/*          The spectral diameter of the matrix. */

	/*  TWIST   (input) int */
	/*          The twist index for the twisted factorization that is used */
	/*          for the negcount. */
	/*          TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T */
	/*          TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T */
	/*          TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r) */

	/*  INFO    (output) int */
	/*          Error flag. */

	/*  Further Details */
	/*  =============== */

	/*  Based on contributions by */
	/*     Beresford Parlett, University of California, Berkeley, USA */
	/*     Jim Demmel, University of California, Berkeley, USA */
	/*     Inderjit Dhillon, University of Texas, Austin, USA */
	/*     Osni Marques, LBNL/NERSC, USA */
	/*     Christof Voemel, University of California, Berkeley, USA */

	/*  ===================================================================== */

	/*     .. Parameters .. */
	/*     .. */
	/*     .. Local Scalars .. */
	/*     .. */
	/*     .. External Functions .. */

	/*     .. */
	/*     .. Intrinsic Functions .. */
	/*     .. */
	/*     .. Executable Statements .. */

	/* Parameter adjustments */
	--iwork;
	--work;
	--werr;
	--wgap;
	--w;
	--lld;
	--d__;

	/* Function Body */
	*info = 0;

	maxitr = (int) ((log(*spdiam + *pivmin) - log(*pivmin)) / log(2.)) + 2;
	mnwdth = *pivmin * 2.;

	r__ = *twist;
	if (r__ < 1 || r__ > *n) {
		r__ = *n;
	}

	/*     Initialize unconverged intervals in [ WORK(2*I-1), WORK(2*I) ]. */
	/*     The Sturm Count, Count( WORK(2*I-1) ) is arranged to be I-1, while */
	/*     Count( WORK(2*I) ) is stored in IWORK( 2*I ). The int IWORK( 2*I-1 ) */
	/*     for an unconverged interval is set to the index of the next unconverged */
	/*     interval, and is -1 or 0 for a converged interval. Thus a linked */
	/*     list of unconverged intervals is set up. */

	i1 = *ifirst;
	/*     The number of unconverged intervals */
	nint = 0;
	/*     The last unconverged interval found */
	prev = 0;
	rgap = wgap[i1 - *offset];
	i__1 = *ilast;
	for (i__ = i1; i__ <= i__1; ++i__) {
		k = i__ << 1;
		ii = i__ - *offset;
		left = w[ii] - werr[ii];
		right = w[ii] + werr[ii];
		lgap = rgap;
		rgap = wgap[ii];
		gap = min(lgap, rgap);
		/*        Make sure that [LEFT,RIGHT] contains the desired eigenvalue */
		/*        Compute negcount from dstqds facto L+D+L+^T = L D L^T - LEFT */

		/*        Do while( NEGCNT(LEFT).GT.I-1 ) */

		back = werr[ii];
		L20: negcnt = pdlaneg(n, &d__[1], &lld[1], &left, pivmin, &r__);
		if (negcnt > i__ - 1) {
			left -= back;
			back *= 2.;
			goto L20;
		}

		/*        Do while( NEGCNT(RIGHT).LT.I ) */
		/*        Compute negcount from dstqds facto L+D+L+^T = L D L^T - RIGHT */

		back = werr[ii];
		L50: negcnt = pdlaneg(n, &d__[1], &lld[1], &right, pivmin, &r__);
		if (negcnt < i__) {
			right += back;
			back *= 2.;
			goto L50;
		}
		width = (d__1 = left - right, fabs(d__1)) * .5;
		/* Computing MAX */
		d__1 = fabs(left), d__2 = fabs(right);
		tmp = max(d__1, d__2);
		/* Computing MAX */
		d__1 = *rtol1 * gap, d__2 = *rtol2 * tmp;
		cvrgd = max(d__1, d__2);
		if (width <= cvrgd || width <= mnwdth) {
			/*           This interval has already converged and does not need refinement. */
			/*           (Note that the gaps might change through refining the */
			/*            eigenvalues, however, they can only get bigger.) */
			/*           Remove it from the list. */
			iwork[k - 1] = -1;
			/*           Make sure that I1 always points to the first unconverged interval */
			if (i__ == i1 && i__ < *ilast) {
				i1 = i__ + 1;
			}
			if (prev >= i1 && i__ <= *ilast) {
				iwork[(prev << 1) - 1] = i__ + 1;
			}
		} else {
			/*           unconverged interval found */
			prev = i__;
			++nint;
			iwork[k - 1] = i__ + 1;
			iwork[k] = negcnt;
		}
		work[k - 1] = left;
		work[k] = right;
		/* L75: */
	}

	/*     Do while( NINT.GT.0 ), i.e. there are still unconverged intervals */
	/*     and while (ITER.LT.MAXITR) */

	iter = 0;
	L80: prev = i1 - 1;
	i__ = i1;
	olnint = nint;
	i__1 = olnint;
	for (ip = 1; ip <= i__1; ++ip) {
		k = i__ << 1;
		ii = i__ - *offset;
		rgap = wgap[ii];
		lgap = rgap;
		if (ii > 1) {
			lgap = wgap[ii - 1];
		}
		gap = min(lgap, rgap);
		next = iwork[k - 1];
		left = work[k - 1];
		right = work[k];
		mid = (left + right) * .5;
		/*        semiwidth of interval */
		width = right - mid;
		/* Computing MAX */
		d__1 = fabs(left), d__2 = fabs(right);
		tmp = max(d__1, d__2);
		/* Computing MAX */
		d__1 = *rtol1 * gap, d__2 = *rtol2 * tmp;
		cvrgd = max(d__1, d__2);
		if (width <= cvrgd || width <= mnwdth || iter == maxitr) {
			/*           reduce number of unconverged intervals */
			--nint;
			/*           Mark interval as converged. */
			iwork[k - 1] = 0;
			if (i1 == i__) {
				i1 = next;
			} else {
				/*              Prev holds the last unconverged interval previously examined */
				if (prev >= i1) {
					iwork[(prev << 1) - 1] = next;
				}
			}
			i__ = next;
			goto L100;
		}
		prev = i__;

		/*        Perform one bisection step */

		negcnt = pdlaneg(n, &d__[1], &lld[1], &mid, pivmin, &r__);
		if (negcnt <= i__ - 1) {
			work[k - 1] = mid;
		} else {
			work[k] = mid;
		}
		i__ = next;
		L100: ;
	}
	++iter;
	/*     do another loop if there are still unconverged intervals */
	/*     However, in the last iteration, all intervals are accepted */
	/*     since this is the best we can do. */
	if (nint > 0 && iter <= maxitr) {
		goto L80;
	}

	/*     At this point, all the intervals have converged */
	i__1 = *ilast;
	for (i__ = *ifirst; i__ <= i__1; ++i__) {
		k = i__ << 1;
		ii = i__ - *offset;
		/*        All intervals marked by '0' have been refined. */
		if (iwork[k - 1] == 0) {
			w[ii] = (work[k - 1] + work[k]) * .5;
			werr[ii] = work[k] - w[ii];
		}
		/* L110: */
	}

	i__1 = *ilast;
	for (i__ = *ifirst + 1; i__ <= i__1; ++i__) {
		k = i__ << 1;
		ii = i__ - *offset;
		/* Computing MAX */
		d__1 = 0., d__2 = w[ii] - werr[ii] - w[ii - 1] - werr[ii - 1];
		wgap[ii - 1] = max(d__1, d__2);
		/* L111: */
	}
	return 0;

	/*     End of DLARRB */

} /* dlarrb_ */
